MAGNOLIA: Matching Algorithms via GNNs for Online Value-to-go Approximation

TL;DR

This paper presents MAGNOLIA, a GNN-based method for online Bayesian bipartite matching that estimates value-to-go to improve matching quality in digital marketplaces, with theoretical and empirical validation.

Contribution

Introduces a GNN approach to approximate value-to-go in online matching, bridging theory and practice for complex decision-making problems.

Findings

GNN effectively estimates value-to-go for matchings

High-quality matchings achieved across various tasks

Local neighborhood aggregation suffices in certain graph distributions

Abstract

Online Bayesian bipartite matching is a central problem in digital marketplaces and exchanges, including advertising, crowdsourcing, ridesharing, and kidney exchange. We introduce a graph neural network (GNN) approach that emulates the problem's combinatorially-complex optimal online algorithm, which selects actions (e.g., which nodes to match) by computing each action's value-to-go (VTG) -- the expected weight of the final matching if the algorithm takes that action, then acts optimally in the future. We train a GNN to estimate VTG and show empirically that this GNN returns high-weight matchings across a variety of tasks. Moreover, we identify a common family of graph distributions in spatial crowdsourcing applications, such as rideshare, under which VTG can be efficiently approximated by aggregating information within local neighborhoods in the graphs. This structure matches the local behavior of GNNs, providing theoretical justification for our approach.